Sentence examples for by defining a norm from inspiring English sources
By defining a norm, particular Banach spaces of functions can be considered.
By denoting (rho xi,e)) simply by (rho xi)), we define a norm function (rho xi) in C^{infty}(Gbackslash{e}) cap C(G)) such that (1) (rho xi) = 0) if and only if (xi= e); (2) (rho xi) = rho xi^{ - 1})); (3) (rho(delta_{lambda}(xi)) = lambdarho xi)), (lambda > 0).
Define a norm by Vert u Vert _{mathcal{C}}=max_{iin{mathbb{N}}_{0,M-1}}bigl{ Vert u Vert, biglVert D_{r}^{gamma-i} u bigrVert bigr}, where (Vert u Vert = sup_{tin I_{chi}^{T}} vert u(t) vert ) and (Vert D_{r}^{gamma-i}u Vert = sup_{tin I_{chi}^{T}} vert D_{r}^{gamma -i} u(t) vert ).
Example 2.2 Let A = C R 1 [ 0, 1 ] and define a norm on by ∥ x ∥ = ∥ x ∥ ∞ + ∥ x ′ ∥ ∞ for x ∈ A. Define multiplication in as just pointwise multiplication.
Now, we define a norm in E by |x|_{omega}=sup_{tgeq0}big| e^{omega t}S t)xbig|.
Now, we define a norm in E by Vert x Vert _{omega}=sup_{tgeq0} biglVert e^{omega t}T t)x bigrVert.
Then, the function on is defined by (1.2). is defines an norm on with respect to (see, [15]).
We point out how inclusivity and normative objectivity can be reconciled, by defining the norm of good design in terms of a deliberative cooperation between designers and the people they design for.
The datum of an inner product entails that lengths of vectors can be defined too, by defining the associated norm |\mathbf v| := \sqrt {\langle \mathbf v, \mathbf v \rangle}.
Practice #1: Increase trust by defining new conversational norms.
